Gaussian characterization of uniform Donsker classes of functions
type: Item
instance of: scholarly article
title: Gaussian characterization of uniform Donsker classes of functions
zbMATH Open document ID: 0734.60007
author: Joel Zinn
author: Evarist Giné
published in: The Annals of Probability
publication date: 1991-01-01T00:00:00Z
review text: The main result of the paper is Theorem. Let \({\mathcal F}\) be a measurable class of functions. Then \({\mathcal F}\) is finitely uniformly pre-Gaussian iff \({\mathcal F}\) is a uniform Donsker class. The authors also obtain an improvement of a theorem of Shehy and Wellner on uniformity of the CLT over subsets of probability measures and prove uniform exponential bounds for empirical processes indexed by universal bounded Donsker and uniform Donsker classes of functions.
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 4215031
zbMATH Keywords: Gaussian characterization
zbMATH Keywords: Donsker class
zbMATH Keywords: uniform exponential bounds for empirical processes
zbMATH Keywords: uniform Donsker classes
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176990450
OpenAlex ID: W1981601376
DOI: 10.1214/AOP/1176990450
description: scientific article; zbMATH DE number 4215031